April 29 2007 6:41:40.960 AM FEM1D_NONLINEAR FORTRAN90 version Solve a nonlinear boundary value problem: -d/dx (p(x) du/dx) + q(x)*u + u*u' = f(x) on an interval [xl,xr], with the values of u or u' specified at xl and xr. The equation is to be solved for X greater than XL = .000000 and less than XR = 1.00000 The boundary conditions are: At X = XL, U= .000000 At X = XR, U'= 1.00000 This is test problem #1: P(X) = 1, Q(X) = 0, F(X) = X. Boundary conditions: U(0) = 0, U'(1) = 1. The exact solution is U(X) = X Number of quadrature points per element is 1 Number of iterations is 10 Node Location 0 .000000 1 .100000 2 .200000 3 .300000 4 .400000 5 .500000 6 .600000 7 .700000 8 .800000 9 .900000 10 1.00000 Subint Length 1 .100000 2 .100000 3 .100000 4 .100000 5 .100000 6 .100000 7 .100000 8 .100000 9 .100000 10 .100000 Subint Quadrature point 1 0.500000E-01 2 .150000 3 .250000 4 .350000 5 .450000 6 .550000 7 .650000 8 .750000 9 .850000 10 .950000 Subint Left Node Right Node 1 0 1 2 1 2 3 2 3 4 3 4 5 4 5 6 5 6 7 6 7 8 7 8 9 8 9 10 9 10 Node Unknown 0 -1 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 Printout of tridiagonal linear system: Equation ALEFT ADIAG ARITE RHS 1 20.0000 -10.0000 0.100000E-01 2 -10.0000 20.0000 -10.0000 0.200000E-01 3 -10.0000 20.0000 -10.0000 0.300000E-01 4 -10.0000 20.0000 -10.0000 0.400000E-01 5 -10.0000 20.0000 -10.0000 0.500000E-01 6 -10.0000 20.0000 -10.0000 0.600000E-01 7 -10.0000 20.0000 -10.0000 0.700000E-01 8 -10.0000 20.0000 -10.0000 0.800000E-01 9 -10.0000 20.0000 -10.0000 0.900000E-01 10 -10.0000 10.0000 1.04750 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .149750 2 .200000 .298500 3 .300000 .445250 4 .400000 .589000 5 .500000 .728750 6 .600000 .863500 7 .700000 .992250 8 .800000 1.11400 9 .900000 1.22775 10 1.00000 1.33250 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 0.849454E-01 2 .200000 .170164 3 .300000 .255932 4 .400000 .342534 5 .500000 .430266 6 .600000 .519437 7 .700000 .610377 8 .800000 .703436 9 .900000 .798989 10 1.00000 .897438 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .105202 2 .200000 .210298 3 .300000 .315181 4 .400000 .419746 5 .500000 .523887 6 .600000 .627501 7 .700000 .730483 8 .800000 .832732 9 .900000 .934149 10 1.00000 1.03464 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100039 2 .200000 .200077 3 .300000 .300111 4 .400000 .400140 5 .500000 .500163 6 .600000 .600179 7 .700000 .700189 8 .800000 .800194 9 .900000 .900195 10 1.00000 1.00020 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Computed solution: Node X(I) U(X(I)) 0 .000000 .000000 1 .100000 .100000 2 .200000 .200000 3 .300000 .300000 4 .400000 .400000 5 .500000 .500000 6 .600000 .600000 7 .700000 .700000 8 .800000 .800000 9 .900000 .900000 10 1.00000 1.00000 Compare computed and exact solutions: X Computed U Exact U .000000 .000000 .000000 .125000 .125000 .125000 .250000 .250000 .250000 .375000 .375000 .375000 .500000 .500000 .500000 .625000 .625000 .625000 .750000 .750000 .750000 .875000 .875000 .875000 1.00000 1.00000 1.00000 FEM1D_NONLINEAR: Normal end of execution. April 29 2007 6:41:40.962 AM